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Angela Mihai

Professor Angela Mihai

Professor of Applied Mathematics, Director of Research

School of Mathematics

Overview

I am a member of the Applied and Computational Mathematics Research Group and Director of Research and Innovation at the School of Mathematics, Cardiff University. I am also a Fellow of the Institute of Mathematics and its Applications (FIMA) and Vice President of the UK and Republic of Ireland Section of the Society for Industrial and Applied Mathematics (SIAM-UKIE).

Publication

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2011

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2009

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2005

Articles

Book sections

Books

Conferences

Research

I have a broad research interest in applied and computational mathematics at the interface between physical and natural sciences. My expertise is in fundamental solid mechanics and the mathematical understanding of soft materials, including multiscale modelling, limit states analysis, optimisation, and uncertainty quantification.

I led externally funded research projects on cellular solids and multi-body systems with applications to biological tissues and soft matter, and made contributions to stochastic elasticity, which is a fast-developing field at the forefront of interdisciplinary research in continuum mechanics. 

My research monograph, “Stochastic Elasticity: A Nondeterministic Approach to the Nonlinear Field Theory”, Springer, 2022, is the first book to combine fundamental large strain elasticity and probability theories. Its aim is to make both theories accessible to scientists wishing to incorporate uncertainty quantification in phenomenological studies of soft materials. It is a modern book that covers classical and more advanced research topics.

An important area of my work is the mathematical modelling of liquid crystal elastomers (LCEs). These are advanced multifunctional materials that combine elasticity with orientational order. Specifically, mechanical strains give rise to changes in liquid crystalline order and changes in the orientational order generate mechanical stresses and strains. Because of their complex material responses in the presence of natural stimuli like heat, light, electric or magnetic fields, LCEs are suitable for a wide range of applications in science, manufacturing, and medical research. This work provides the foundation for further mathematical modelling of self-organisation in active biological matter.

Visit Google Scholar, MathSciNetORCID, and ResearchGate .

Mottoes to papers

  • "The task of the theorist is to bring order into the chaos of the phenomena of nature, to invent a language by which a class of these phenomena can be described efficiently and simply." - C. Truesdell (1965) (doi: 10.1098/rspa.2017.0607)
  • "This task is made more difficult than it otherwise would be by the fact that some of the test-pieces used have to be moulded individually, and it is difficult to make two rubber specimens having identical properties even if nominally identical procedures are followed in preparing them." - R. S. Rivlin & D. W. Saunders (1951) (doi: 10.1007/s42558-019-0013-1)
  • "Instead of stating the positions and velocities of all the molecules, we allow the possibility that these may vary for some reason - be it because we lack precise information, be it because we wish only some average in time or in space, be it because we are content to represent the result of averaging over many repetitions [...] We can then assign a probability to each quantity and calculate the values expected according to that probability." - C. Truesdell (1984) (doi: 10.1177/1081286520914958)
  • "It is a problem of mechanics, highly complicated and irrelevant to probability theory except insofar as it forces us to think a little more carefully about how probability theory must be formulated if it is to be applicable to real situations.” - E. T. Jaynes (1996) (doi: 10.1088/1361-6544/ab7104)
  • "Denominetur motus talis, qualis omni momento temporis t praebet configurationem ca- pacem aequilibrii corporis iisdem viribus massalibus sollicitati, ‘motus quasi aequilibratus’. Generatim motus quasi aequilibratus non congruet legibus dynamicis et proinde motus verus corporis fieri non potest, manentibus iisdem viribus masalibus.” - C. Truesdell (1962) (doi: 10.1093/imatrm/tnz003)
  • “Of particular relevance here is the fact that technology of people must be different from that of nature simply because the two span different size scales [...] Everyday terms such as ‘assembly’, ‘polymer’, ‘blueprint’, ‘safety factor’, ‘design’, and ‘intended application’ were meant for our production systems, and we run considerable risk of self-deception when we use them for natural systems.” - S. Vogel (1998) (doi: 10.1007/s42558-023-00051-y)

Funded projects

  • Learning macroscopic models for multibody systems of hyperelastic materials, Research in Groups, International Centre for Mathematical Sciences (ICMS), Edinburgh (2024), Supported by EPSRC Grant EP/R015007/1 
  • Pattern formation in soft materials: reduced models and nonlinear analysis, HORIZON-MSCA-2022 Postdoctoral Fellowship to Dr Yang Liu, University of Oxford, UK (2023 - 2025)
  • Mathematical modelling and numerical analysis of liquid crystal elastomers, Full PhD studentship, College of Physical Sciences and Engineering, Cardiff University (2022 - 2026)
  • Limit analysis of debonding states in multi-body systems of stochastic hyperelastic material, EPSRC Grant EP/S028870/1 (2019 - 2022)
  • Debonding and stretching of biogenic cellular structures, Full PhD studentship, College of Physical Sciences and Engineering, Cardiff University (2015 - 2019)
  • Limit analysis of collapse states in cellular solids, EPSRC Grant EP/M011992/1 (2015 - 2017)

Events organisation

Video recordings

Cover image

ECMI blog posts

 

 

Teaching

I am a fellow of the UK Higher Education Academy. My teaching at Cardiff University is in Applied Mathematics.

Courses taught

  • Introduction to Mathematical Modelling of Liquid Crystal Elastomers
    • PhD-level Mathematics (2023 - 2024)
  • Numerical Analysis
    • Year 2 Mathematics (2013 - Present)
  • Finite Elasticity
    • Year 3 Mathematics (2020 - 2022)
    • Year 4 MMath (2015 - 2020)
  • Classical Mechanics
    • Year 1 Mathematics (2012 - 2017)

I offer a range of projects to final year undergraduate students and to year 12 students on Nuffield Research Placements and Experiences Programme.

Biography

Career overview

I started my mathematical journey as an undergraduate student at the University of Bucharest, Romania. I later continued my studies with a Part III of the Mathematical Tripos at the University of Cambridge, UK, funded by a full Shell Centenary Scholarship awarded by Shell Group and Cambridge University Trust. In 2005, I earned my PhD for research in numerical analysis from the University of Durham, UK. I then expanded my expertise as a postdoctoral researcher at the Universities of Strathclyde, Cambridge, and Oxford, focusing on mathematics and mechanics of solids, where there was a need for mathematicians to specialise in this key interdisciplinary field. I joined Cardiff University as a Lecturer in 2011 and steadily progressed to my current academic role.

Professional memberships

Committees and reviewing

Supervisions

Postdoctoral researchers

Current supervision

Rabin Poudel

Rabin Poudel

Research student

Past projects

Contact Details



Campuses Abacws, Room 5.14, Senghennydd Road, Cathays, Cardiff, CF24 4AG

Research themes

Specialisms

  • Applied mathematics
  • Numerical analysis
  • Solid mechanics